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We prove that the Leray spectral sequence in rational cohomology for the quotient map Un,d → Un,d/G where Un,d is the affine variety of equations for smooth hypersurfaces of degree d in P(C) and G is the general linear group, degenerates at E2.

We study the relation between a certain graded part of the Jacobian ring of a projective hypersurface and a certain graded quotient for the Hodge filtration of its primitive cohomology, in the case that the hypersurface has at most isolated singularities. We distinguish a class of singularities for which this relation is best possible. The main examples… (More)

- J H M Steenbrink
- 1995

We consider a mixed Hodge moduleM on a normal surface sin gularity X x and a holomorphic function germ f X x C For the case that M has an abelian local monodromy group we give a formula for the spectral pairs of f with values in M This result is applied to generalize the Sebastiani Thom formula and to describe the behaviour of spectral pairs in series of… (More)

We give a survey of properties of the monodromy of local systems on quasi-projective varieties which underlie a variation of Hodge structure. In the last section a less widely known version of a NoetherLefschetz type theorem is discussed.

- R. H. Jeurissen, C. H. van Os, J. H. M. Steenbrink
- Discrete Mathematics
- 1994

- J H M Steenbrink
- 1999

Let X be a complete complex algebraic variety of dimension n and let D be a divisor with strict normal crossings on X. In this paper we show that the cup product maps H (X \ D) ⊗ H(X, D) → H(X, D) and H i D(X) ⊗ H (D) → H D (X) are morphisms of mixed Hodge structures.

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